School Improvement and Governance Network

Big Ideas

Maths and science learning - discussion paper

Following further feedback and amendments from many people, this paper was last updated on 6 April 2012. We also invite you to provide your feedback about this latest draft. We wish to thank the principals, teachers, parents, students, researchers and personnel in the Victorian Department of Education and Early Childhood Development who commented on previous drafts of this paper.

Introduction

Key questions in the on-going development of high-quality maths and science education include:

  • How best to further build equity, quality and participation in maths and science learning in schools
  • How best to develop school community conversations and planning around maths and science learning
  • How best, therefore, to improve learning outcomes for all students and reduce the achievement gap.

There have long been concerns about the declining proportion of Australian students who elect to study maths and science subjects in the senior years of secondary school. Student participation in maths and science emerges as a challenge in the middle years and, later, universities suffer from declining enrolments in the physical, chemical and mathematical sciences.

As well, in the Trends in International Mathematics and Science Study (TIMSS), for Year 4 maths, 41 per cent of Victorian students achieved at or above the high international benchmark. In comparison, 81 per cent of Hong Kong students met this standard. Likewise, in Year 4 science, Victoria (with 49 per cent) had the highest percentage of students of any Australian state or territory at or above the high international benchmark. In comparison, in Singapore 68 per cent of students met this standard.

Achievement in maths and science is closely related to the social background of students. This has an impact not only by way of the extreme variation in learning outcomes. Students from lower SES backgrounds can also be six to eight times less likely than students from higher SES backgrounds to enroll, for example, in specialist maths. This is unacceptable in the 21st century!

To help to address these challenges, VICCSO has been compiling examples from schools of practical strategies for improvement. VICCSO has a particular emphasis on strategies that educators, families, school councils and community organisations can co-support to improve maths and science outcomes for all. There are four key areas that focus attention on the good practices of schools and education systems. These are:

  1. Leadership and school partnerships
  2. Teaching, learning and the curriculum
  3. A P-12 approach to maths and science
  4. Learning facilities and infrastructure.

The following discussion of these four areas is informed by the ideas and experiences of many schools. This discussion also draws upon, complements and adds value to the Department's Energising Science and Mathematics paper.

1. Leadership and school partnerships

Leadership in maths and science learning is about setting directions, influencing thinking and practice and helping to develop a community of maths and science teacher learners/leaders. It also includes building stronger school-family-community partnerships and supporting parents and students to be school leaders through, for example, school councils and the work of students as leaders of maths and science learning. In their study of maths and science teachers, Miller, Moon & Elko (2000) described teacher leadership as:

“Actions by teachers outside their classroom that involve an explicit or implicit responsibility to provide professional development to their colleagues, to influence their communities’ or districts’ policies, or to act as adjunct staff to support changes in classroom practices among teachers”.

Leaders of maths and science learning

As we have seen in many schools - and notwithstanding the enormous time and resource constraints on any one school's capacity to do all these things consistently, leaders in maths and science include educators, principals and others who:

  • Work with peers and with students and parents on a whole school maths and science strategy or in a cluster of primary and secondary schools (P-12 schooling) or a network
  • Identify and use maths and science learning opportunities in everyday life situations and community settings
  • Build strong maths and science research-practice links and professional networks
  • Build partnerships with kindergartens and colleges/universities
  • Develop good practice in maths and science school-family-community partnerships
  • Lead partnerships to understand and protect ecosystems (e.g., schools involved in replanting areas and promoting biodiversity).

It also involves principals and teachers who seek to influence systemwide educational policy in maths and science through involvement in the relevant professional associations and organisations such as the AEU, VASSP, VPA and VICCSO.

The pivotal role of a school council or board

The strong partnerships built through school councils can also support maths and science learning. Practical initiatives include:

  • Promoting stronger home-school links with families to support maths and science learning at home
  • Investing in programs such as Mathletics
  • Developing a school-family-community conversation and policy in relation to maths and science education.

Schools obviously have some form of two-way communication with students' homes. However, this can often mean providing information to parents about maths and science learning rather than parent input into educational policy decision making. In this respect, among the challenges that educators, principals and school councils mention are:

  • The development of a coherent, whole-school maths and science policy and action plan (as part of a school's strategic plan as co-developed by teachers, parents and students)
  • The development of school strategic plans that include shared school-family-community goals such as the goal that all students have plentiful opportunities to explore the depth of mathematical and scientific understanding across all educational settings: in classrooms, homes and the community
  • How best to build really inclusive, participatory family-school-community partnerships around maths and science learning (especially in school communities with families of culturally and socially diverse background)
  • How local community organisations (e.g., sporting clubs) can be involved - to provide real world experiences and applications of maths and science concepts.

A school council maths and science policy can obviously bring these kinds of issues to the fore and help to ensure that there is a whole school community approach to improvement.

How to develop a whole school community approach

An education or teaching and learning sub-committee of a school council can inform educators' professional knowledge and help to drive thinking about the on-going development of powerful learning in maths and science. It can bring together teachers, parents, students and critical friends to:

  • Exchange information and share experiences and perspectives
  • Pose questions and clarify viewpoints
  • Look at how the curriculum and learning can become more culturally and socially inclusive, which may culminate in a Cultural and Social Inclusion Policy and Plan
  • Jointly explore the best available educational research
  • Through this process, begin to develop a shared, school community policy framework for 21st century education.

As part of this, schools may organise a professionally facilitated forum in which teachers, parents and students are involved in exploring key questions such as:

  • In examining the future of maths and science learning, what fundamental problems are we trying to solve?
  • What do maths and science learning of the future and schooling of the future look and sound like?
  • What is ‘next practice’ in building strong school-family-community learning partnerships?

These kinds of questions may prompt many ideas and insights - which an education sub-committee and school council can build into a shared framework for powerful learning.

2. Teaching, learning and the curriculum

Over many decades, teachers’ pioneering work combined with extensive research have illuminated how students learn in areas such as maths and science and the types of teaching tools and methods that are conducive to such learning. But major challenges remain: besides the achievement gap, many students can be disengaged from maths and science. A broad, unified view of learning is imperative.

Educators seek to avoid the old either-or thinking such as student understanding of Maths (and the cumulative conceptual depth of this knowledge and understanding) versus skills and drills and practical strategies to build students’ memory of problem-solving. There is obviously a place for both! Similar false dichotomies include student engagement versus powerful, in-depth learning. What this means in practice needs to be carefully teased out at the classroom level. As Professor David Clarke points out:

“Dichotomies such as teacher-centred versus student-centred classrooms, real-world versus abstract tasks, and even teaching versus learning can restrict mathematics educators and educational theorists in general to a fragmented view of the mathematics classroom. Constructing such dichotomies as oppositional offers a set of false choices, sanctifying one alternative, while demonising the other".

He thus suggests that:

"International research offers insight into possible explanatory frameworks within which such choices are no longer oppositional or even dichotomous, but rather can be seen as complementary. The acceptance of such complementarities is a first step to an integrative theory of classroom practice and learning”.

An intregrative classroom approach

How is an integrative approach to classroom practice developed? Professional conversations among educators focus attention on both effective classroom practice and the bigger picture of:

  1. Pedagogy - the very best educational values, theories and philosophies, visions and goals, evidence and research and policies that help to tackle challenges such as how best to engage students with meaningful situations within the home and community environments and select appropriate maths and science concepts to understand and solve the task
  2. Information and communication technologies - as a means of individual and collective expression, experience, inquiry, understanding and interpretation and the capacity to use digital technologies to make maths and science learning more profound, accessible and interesting to students, including via the use of realistic data and examples
  3. The depth and coherence of curriculum content - for example, when educators and clusters of schools look at what is already in place and what else can be done to build a coherent P-12 approach to maths and science and seamlessly combine academic knowledge, concepts, theories and principles with applied learning and real world problem solving.

Supported by the requisite resources and on-going professional learning, it is the mix of advances in pedagogy, technology and curricula that puts the ‘power’ into powerful learning experiences for all students and reduces the achievement gap. The challenge (at the school and classroom levels) is thus obviously how best to integrate all three. Punya Mishra and Matthew Koehler and others are researching the mix of pedagogy, technology and content. They use the term ‘TPACK’ or Technological Pedagogical Content Knowledge to describe it.

TPACK can serve to shape broad agreement among maths and science educators as to which practices - when combined - are most likely to improve learning outcomes for all students.

Concept maps

In conjunction with TPACK and e5, concept maps are a powerful tool for maths and science teaching and learning - and many maths and science educators have pioneered their use. Karoline Afamasaga Fuata'i and Greg McPhan in their paper entitled Concept Mapping and Moving Forward as a Community of Learners discuss how concept maps provide:

  • Opportunities to engage in professional development and a collaborative way to actively explore new teaching ideas
  • A tool that can be used by teachers and students alike to organise and reflect on their knowledge and skills.

Researchers such as Jean Schmittau document how concept mapping assists educators to grasp maths as a conceptual system. Concerned that concept mapping in maths has been underutilised, in a paper entitled Uses of Concept Mapping in Teacher Education in Mathematics, Schmittau observes:

"This is unfortunate, since it has the potential to begin to counteract the superficial treatment of concepts occasioned by the failure to develop a coherent curriculum that identifies essential concepts and probes them in sufficient depth".

Many maths and science educators in Victoria have long used concept mapping and other tools to improve learning and develop the depth and coherence of the curriculum. It would be useful to develop better ways to share such experiences.

A broad, unified view of learning

Supported by frameworks such as TPACK as well as tools such as concept maps in guiding the development of instructional practice, maths and science teachers are often at the forefront of tackling old dichotomies in education. They look at how best to further move beyond the divisions between theory and practice, instruction and inquiry-based learning and academic knowledge and practical skills and drills - in order to improve the quality of learning outcomes and the access of students to academic learning by better exploiting these links.

Groves (2008) describes in a study how science teachers were especially adept at catering to students’ lives, interests and experiences, collaborative work, the use of problem solving and the interweaving of the concrete and abstract.

A research project in Melbourne also documented the work of how many science teachers were whole school leaders in making classroom learning real by consistently bringing in practical examples to explain and elucidate scientific concepts.

Consistently linking theory and practice

These educators do not teach key concepts only at the theoretical level, but are always moving backwards and forwards between deep theory and concepts, on the one side, and practical application, skills and real world problem solving, on the other. The project also posed the challenge of what schools can do to best support all staff to more systematically link academic and vocational learning, abstract theory and ‘real world’ application, strong guided instruction and inquiry-based learning, depth of knowledge and practical, hands-on skills.

Such work challenges the old separation of students into academic and vocational, practical and technical tracks. This is obviously important - as maths and science subjects can still be perceived by many students as something solely for the academically ‘able’. Yet, as long led by educators, the very best maths and science learning invariably has both academic, conceptual and theoretical and vocational, practical, skill-based and technical components, which challenges some old either-or views about students’ individual learning styles as being either abstract or concrete.

A socially inclusive curriculum seamlessly combines deep academic knowledge, concepts, theories and principles with applied learning and real world problem solving. The curriculum is then opened up to a wider range of students who may otherwise be streamed into narrowly academic and applied learning and technical pathways.

This work also challenges some types of 'ability' groupings, which if strongly correlated with students' social backgrounds may have a negative effect on the performance of most students (Clarke & Clarke, 2008). There is obviously a need for the most capable students to be provided with high-level challenges in their learning, but care has to be taken to prevent early-onset streaming that may negatively impact upon student participation rates in maths and science later in their education.

Technology in maths and science learning

Young people use information and communication technology (ICT) as a means of individual and collective expression, experience, inquiry, understanding and interpretation. Students are also acquiring new learning preferences and strengths and weaknesses (new technology is double-edged) such as:

  • Expecting to be able to find what they want online whenever they want it
  • Pursuing non-linear, hyper-linked, sometimes discontinuous paths to explore ideas and information
  • Favouring jumping around or taking a serendipitous route to achieve something rather than a more linear, methodical approach to problem solving
  • Preferring problems and learning that blend the abstract and the concrete/specific, the theoretical and the ‘real world’
  • Seeking, sieving and synthesising multiple sources of knowledge and information rather than locating and absorbing information from a single source.

Of the utmost importance for the future of maths and science learning and as is being addressed by many maths and science educators, two major challenges follow.

The first is to understand more about how students are changing (and also are becoming change agents) through their use of ICT - how they think, learn, find, play, make judgments, interact with others and become engaged in the life of their families, schools, communities and societies. The second is, given that young people are inundated by enormous amounts of data that they must access, manage, integrate, and evaluate, how educators can best support students to separate deeper learning and knowledge from superficial fact-gathering.

3. P-12 approach to maths and science

The very future of effective maths and science education pivots on a coherent P-12 approach to schooling! (See the P-12 education partnerships section on this website). P-12 schooling takes shape when a small number of primary and secondary schools work in a cluster and learning community toward a shared pedagogy and a coherent curriculum.

Research in Victoria supports the idea of a unified P-12 approach to curricula, which evolves via teams of teachers developing a shared framework for 21st teaching and learning and increasingly planning and integrating the curriculum from a P-12 perspective. The on-going development of P-12 schooling stands in stark contrast to what Bill Stringer describes as the:

“Two cultures [that] dominate schooling: a primary culture and a secondary culture. Both have sound ideas about the ways for thinking about curriculum and learning in their schools but, when placed together, they make nonsense of the learning continuum with which each of their students is involved.”

While this is not true with many schools (that have long worked to blend primary and secondary school cultures and teaching methods), a continuum of learning and development (including from kindergarten through to university and college) is the next big thing. Initiated by the Country Education Project and sponsored by the Department, the main findings of this research project (2007) are:

  • A more unified P-12 approach to teaching, learning and the curriculum is needed, but this would take a significant policy and operational shift
  • The research literature and the experience of many schools suggest that this shift can significantly improve learning outcomes for all students.

How educators develop a P-12 model

To develop a P-12 approach within a P-12 school or across a cluster of primary and secondary schools, teams of teachers use:

  • Throughlines (i.e., the greater in-depth coverage of fewer topics, ideas, understandings and concepts in the curriculum across the early, middle and later years)
  • P-12 spiral learning built around these throughlines (e.g., see the Wisconsin Organising the Social Studies Curriculum)
  • A mix of both inquiry-based, activity-based and discovery maths and science programs and a teacher’s strong guided instruction focused on deep content.

What this can obviously lead to is a much more coherent P-12 maths and science strategy. However, notwithstanding the many good practices, more work is required to develop coherent maths and science education across the P-12 learning continuum. Middle years work in clusters of primary and secondary schools has, of course, long provided a basis for further progress toward P-12 schooling. It does this through:

  • Links between secondary schools and their feeder primary schools to smooth the transition
  • Visits of primary school students to secondary school laboratories for special science projects
  • Mentoring of primary students by secondary students
  • Supporting teachers across the primary-secondary divide to work together.

A concept-based P-12 curriculum

Schools have also made use of Lynn Erickson's concept-based curriculum planning and concept mapping tools to support P-12 and other curriculum reoganisation and planning. Key concepts in maths and science can be a teacher's lens for developing a coherent curriculum - including across the old primary-secondary divide. Besides educators making use of these curriculum tools, parents and students respond positively to a curriculum that:

  • Shows in advance what students need to know, do and understand to be effective learners in maths and science
  • The knowledge base of maths and science: the content, concepts and understandings essential to each level
  • The skills and drills that students need to acquire and which underpin improvements in their performance.

Such information can be presented visually and succinctly - to assist parents and students to better understand and to better support a coherent P-12 curriculum.

4. Learning facilities and infrastructure

The ideas discussed here obviously require adequate resources and support for schools by education systems. This is a matter of fully funded plans (as well as resources for professional learning support) for maths and science education across the P-12 learning continuum.

A P-12 approach also provides students in the early years with greater access to facilities such as science laboratories. It is also a matter of new school building designs and infrastructure (including specialist maths and science areas, hardware and high speed broadband) supporting maths and science learning.

Specialist maths and science facilities also serve to foster contemporary teaching and learning practices. Video-conferencing facilities, for example, can deliver high-quality teaching, create virtual communities of educators across the P-12 spectrum and provide real-time interaction and assessment.

Some of the best work involves teachers coordinating learning activities (e.g., sustainability work) outside of the school. However, to become mainstream forms of powerful learning, such activities also require adequate resources and support.

What is also required is wider-spread advocacy to 'get the word out' about the future of maths and science education and being more effective in lobbying for the changes and resources that are needed to work toward educational improvement.

Conclusion

The practical things that we - as teachers, parents, principals, students and community members - can all do to improve maths and science education can be grouped into four key areas:

  1. Leadership and school partnerships
  2. Teaching, learning and the curriculum
  3. A P-12 approach to maths and science
  4. Learning facilities and infrastructure.

Although it is obviously impossible to work on all of these things at any one time, each of these four areas informs the ideas and actions embodied in the other three and thus creates a total effect.